<p>This paper investigates adaptive formation control for multi-agent systems with nonlinear dynamics and uncertainties within a ratio-of-distance (RoD) rigidity framework. Distributed control laws are developed to achieve and maintain rigid formation shapes while tracking prescribed maneuvering velocities in both time-invariant and time-varying cases. The RoD-based formulation enables formation stabilization using only relative distance ratios, providing a scalable description of rigid shapes. To improve practical efficiency, an event-triggered control strategy is incorporated. In the proposed approach, each agent monitors its own states and the current states of its neighbors while updating its control input only when necessary. Adaptive terms within the distributed controller compensate for uncertainties in the agent dynamics. For maneuvering tasks with time-varying desired velocities, nonsmooth control terms are introduced to handle velocity variations. Lyapunov-based analysis is carried out to examine the stability of the closed-loop system. It is shown that, under suitable control gains, the formation errors asymptotically converge to zero while all adaptive signals remain bounded. Sufficient conditions on the controller parameters and event-triggering functions are derived to ensure asymptotic formation stabilization and velocity consensus. Simulations confirm the effectiveness of the proposed method under uncertain dynamics with significantly fewer control updates compared with continuous-time control.</p>